What is the square of a column vector?

[devonho]

Homework Statement

Hi,

Is there a matrix property that can be applied to take the square of a column vector?

Something like:

${\bf x}=\left[x_1,x_2,x_3\right]^T$
$\left[{\bf x}\right]^2$
$={\bf x}{\bf x}^T$
or
$={\bf x}^T{\bf x}$?

Thank you.

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

Hi,

Is there a matrix property that can be applied to take the square of a column vector?

Something like:

${\bf x}=\left[x_1,x_2,x_3\right]^T$
$\left[{\bf x}\right]^2$
$={\bf x}{\bf x}^T$
or
$={\bf x}^T{\bf x}$?

Thank you.
...

What is the size of the matrix: $={\bf x}{\bf x}^T\,?$

What is the size of the matrix: $={\bf x}^T{\bf x}\,?$

 

[devonho]

Hi SammyS,

${\bf x}{\bf x}^T$ is 3x3
while
${\bf x}^T{\bf x}$ is 1x1

 

[murmillo]

I'm not sure what you mean by the square of a column vector...

 

[SammyS]

Generally the square of a vector refers to the scalar product, which you can crudely think of as a 1 by 1 matrix. Therefore, the answer is (x^T)x .